The influence of constant axial compression pre-stress on the fatigue failure of torsion loaded tube springs

This paper reports the results of a series of biaxial static compression and torsion experiments performed to evaluate the effects of static compression stress on the fatigue life those smooth tubes made of high strength spring steel. Compression pre-stress was introduced by a solid steel bar inserted into a hollow spring and loaded with a screw-joint. The experimentally obtained results show a significant extension of fatigue strain life as a result of combining axial compression loading with torsion. Cracking behavior was observed and it was noted that compression pre-stresses contribute to retardation of the fatigue crack initiation process and, consequently, contribute to the extension of fatigue life. The fatigue shear crack initiated in a transverse direction. This crack continues to propagate in the same direction until it starts to propagate as a macro-crack on the maximum shear plane.     

Constitutive modeling of powder metallurgy processed Al–4%Cu preforms during compression at elevated temperature

In this study, a hot deformation constitutive base analysis has been conducted on powder metallurgy (P/M) processed Al–4%Cu preforms. The main objective is to evaluate the effect of initial relative density on the hot deformation behaviour and to establish the constitutive equation which considers the effect of initial relative density during hot compression test. This has been carried out by using the true stress–true strain curve data obtained from hot compression test of P/M processed Al–4%Cu preforms with different initial relative density of 0.84, 0.87 and 0.9 for various range of temperature 300–500 °C and strain rate range of 0.1–0.4 s⁻¹. It has been found that the flow stress is notably influenced by initial relative density, temperature and strain rate. The results show that the flow stress exhibits peak value at certain strain value, and then decreases showing flow softening until the flow stress remains constant at higher strain values. A constitutive equation that predicts the flow stress in hot compression of P/M processed Al–4%Cu preforms has been developed. The predicted flow stress values are in a good agreement with the experimental results and it is confirmed that the formulated constitutive equation is accurate and reliable to predict the flow stress of Al–4%Cu preforms during hot compression at elevated temperature.     

Microstructural aspects and modeling of failure in naturally occurring porous composites

Results from an experimental investigation on the compression behavior of balsa wood are presented. Specimens with varying densities, ranging from 55 to 380 kg/m³, are loaded in the grain (fiber, cell) direction using a screw-driven material testing system at a strain rate of 10⁻³ s⁻¹. The results indicate that compressive strength of balsa wood increases with increasing density. Post-test scanning electron microscopy is used to identify the failure modes. The failure of low-density specimens is governed by elastic and/or plastic buckling, while kink band formation and end-cap collapse dominate in higher density balsa specimens. Based on the experimental results and observations, several analytical models are proposed to predict the compressive failure strength of balsa wood under uniaxial loading conditions.     

Biaxial fatigue for proportional and non‐proportional loading paths

In order to study the use of a local approach to predict crack‐initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto‐plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue‐life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain‐based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress‐invariant‐based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress‐invariant parameter with non‐proportional factors correlated well with the experimental results obtained in this study.     

An experimental study of failure and softening in sand under three-dimensional stress condition

This paper describes an experimental study of failure and softening behaviour in dense Toyoura sand. A true triaxial apparatus equipped with three pairs of rigid loading platens is used to test sand sample under three-dimensional stress condition. The testing results demonstrate that the rigid boundary around the sand samples cannot prevent formation of shear localization. Shear localization are observed to emerge in the hardening or the softening regime in the loading depending on the magnitude of intermediate principal stress. Uniform deformation for the whole strain range is obtained only in triaxial compression tests. The peak stress state obtained from tests of sand samples of the same initial density can be described with good approximation by the Matsuoka–Nakai criterion.     

Ratchetting behavior of advanced 9-12% chromium ferrite steel under creep-fatigue loadings

The ratchetting behavior of advanced 9-12% chromium ferrite steel was investigated by cyclic loading tests with various hold times and stress ratios at elevated temperature of 873 K. Particular attention was paid to the effect of hold time on the whole-life ratchetting deformation and failure mechanism. Results indicate that the total ratchetting strains under creep-fatigue loading can be decomposed into two parts, i.e., cyclic accumulated creep strain produced during the peak stress hold time (ε_R1), cyclic accumulated inelastic strain produced during the stress change process (ε_R2). A transition in ratchetting components and rupture behavior with the increase of hold time was observed. In the long hold time domain, a quick shakedown of ratchetting strain ε_R2 occurs after the very first few cycles and the rupture behavior is fully controlled by the time-dependent creep damage. In the short hold time domain, ratchetting strain ε_R2 increases till the specimens fails and a mixed damage mode is responsible for the failure. An attempt is made to explain the existence of these two domains in terms of the evolutions of three internal stress components (back stress, isotropic stress and viscous stress) measured at the end of the holding period.     

Size effect of concrete members applied with flexural compressive stresses

In this study, two types of special experiments are carried out to understand flexural compressive strength size effect of concrete members. The first type is an ordinary cylindrical specimen (CS) with a fully penetrated and vertically standing plate type notch at the mid-height of the specimen, which is loaded in compression at the top surface (e.g., in the parallel direction to the notch length). The second type is a general double cantilever beam (DCB), which is compression loaded in axial direction (e.g., in the parallel direction of the notch). For CS, an adequate notch length is taken from the experimental results obtained from the compressive strength experiment of various initial notch lengths. The trial tests to select the effective initial notch length show that CS with an initial notch length approximately greater than four times the maximum aggregate size fails without an additional increased load and in stable manner under Mode I failure mechanism. Therefore, the initial notch length to the maximum aggregate size ratio of 4.0 is used for all size specimens. For DCB, the eccentricity of loading points with respect to the axial axis of each cantilever and the initial notch length are varied. In both specimens, the compressive loads apply flexural compressive stresses on the crack tip region of the specimens. These two types of specimens fail by Mode I crack opening mechanism. By testing 3 geometrically proportional size specimens for CS and DCB, the experimental datum for flexural compression size effect of concrete are obtained. Using the obtained flexural compressive strength size effect datum, regression analyses are performed using Levenberg-Marquardt's least square method (LSM) to suggest new parameters for the modified size effect law (MSEL). The analysis results show that size effect is apparent for flexural compressive strength of specimens with an initial notch. For CS, the effect of initial notch length on flexural compressive strength size effect is apparent. For DCB, flexural compressive size effect is dependent on the eccentricity of loading points with respect to the axial axis of the cantilever beam. In other words, if DCB specimen is applied with greater tensile stress at the crack tip, the size effect of concrete becomes more distinct. The results show that the flexural compressive strength size effect of initial notch length variation of DCB exists but directly dependent on the loading location. This is due to the fact that the sizes of fracture process zone (FPZ) of all DCB specimens are similar regardless of the differences in the specimen slenderness ratio, but the flexural compressive and tensile stress combinations resulting in stress concentration at the crack tip region has direct effect on size effect of concrete members.     

钢管混凝土轴心受压构件的徐变预测模型及其徐变性能分析

为研究混凝土徐变对钢管混凝土轴心受压构件长期受力性能的影响,考虑构件截面内力重分布,建立了钢管混凝土轴心受压构件截面应力和应变以徐变系数为参数的随混凝土龄期变化关系的理论模型,结合已有试验数据和国内外常用12种混凝土徐变预测模型对该模型进行验证,并找到了适用于钢管混凝土轴心受压构件的徐变预测模型--Huo模型;在此基础上,计算并分析了钢管混凝土轴心受压构件混凝土龄期为10000 d的截面应力和应变;通过对混凝土强度等级、环境年平均相对湿度、初始加载龄期、含钢率、构件长度、截面应力水平等因素的不同取值,分析了各因素对钢管混凝土轴心受压构件徐变性能的影响程度及规律。结果表明:当钢管混凝土轴心受压构件的轴力不大于其极限承载力的60%时,随着加载龄期的增长,钢管截面应力逐渐增大,最大变化量达61.4%,而混凝土截面应力逐渐减小,最大变化量达26.2%;加载初期构件应变增长迅速,1000 d以后应变增长速度减慢,构件最终应变是初始应变的1.61倍;在轴压比相同的条件下,钢管混凝土轴心受压构件的徐变应变终值随着混凝土强度等级的提高而逐渐增大,随着含钢率的增大显著减小,随着初始加载龄期、环境年平均相对湿度、构件长度的增大而逐渐减小,轴压比不大于0.6时,其徐变应变终值随轴压比增长。研究成果可为钢管混凝土轴心受压构件在正常使用阶段徐变计算以及徐变变形控制提供依据。     

Cyclic modeling of FRP-confined concrete with improved ductility

Confinement by fiber reinforced polymer (FRP) wraps can significantly enhance strength and ductility of concrete columns. Behavior of FRP-confined concrete in uniaxial compression can be characterized by its bilinear stress–strain and unique dilation properties. A number of models have in recent years been developed to capture these characteristics under monotonic loading. None, however, have addressed the cyclic response of FRP-confined concrete. A total of 24 FRP-confined concrete stub specimens were tested in uniaxial compression under different levels of loading and unloading, with different fiber type, wrap thickness, and loading patterns. Based on a regression analysis of test results, a constitutive model is developed that includes cyclic rules for loading and unloading, plastic strains, and stiffness and strength degradations. The proposed model is validated by comparing analytical predictions with experimental results of an independent test series. Good agreement was shown between the analysis and experiments, confirming the ability of the model to predict the cyclic behavior of FRP-confined concrete. The model could be easily implemented in a fiber element model for flexural analysis of cyclic loaded beam-columns in conjunction with a strain gradient approach.     

Fatigue strength of notched specimens made of 40CrMoV13.9 under multiaxial loading

The work deals with multiaxial fatigue strength of notched round bars made of 40CrMoV13.9 steel and tested under combined tension and torsion loading, both in-phase and out-of-phase. The axis-symmetric V-notches present a constant notch root radius, 1 mm, and a notch opening angle of 90°; the notch root radius is equal to 4 mm in the semi-circular notches where the strength in the high cycle fatigue regime is usually controlled by the theoretical stress concentration factor, being the notch root radius large enough to result in a notch sensitivity index equals to unity. In both geometries the diameter of the net transverse area is 12 mm.The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. Altogether more than 120 new fatigue data are summarised in the present work, corresponding to a one-year of testing programme.All fatigue data are presented first in terms of nominal stress amplitudes referred to the net area and then re-analysed in terms of the mean value of the strain energy density evaluated over a given, crescent shape volume embracing the stress concentration region. For the specific steel, the radius of the control volume is found to be independent of the loading mode.     

Comparative study on biaxial low-cycle fatigue behaviour of three structural steels

In this study the uniaxial/biaxial low‐cycle fatigue behaviour of three structural steels (Ck45 normalized steel, 42CrMo4 quenched and tempered steel and AISI 303 stainless steel) are studied, evaluated and compared. Two parameters are considered for estimating non‐proportional fatigue lives: the coefficient of additional hardening and the factor of non‐proportionality. A series of tests of uniaxial/biaxial low‐cycle fatigue composed of tension/compression with cyclic torsion were carried out on a biaxial servo‐hydraulic testing machine. Several loading paths were carried out, including proportional and non‐proportional ones, in order to verify the additional hardening caused by different loading paths. The experiments showed that the three materials studied have very different additional hardening behaviour. Generally, the transient process from the initial loading cycle to stabilized loading cycle occurs in a few cycles. The stabilized cyclic stress/strain parameters are controlling parameters for fatigue damage. A factor of non‐proportionality of the loading paths is evaluated based on the Minimum Circumscribed Ellipse approach. It is shown that the microstructure has a great influence on the additional hardening and the hardening effect is dependent on the loading path and also the intensity of the loading.     

Quasistatic and dynamic crushability of polymeric foams in rigid confinement

An approach was developed for investigating the crushability behavior of epoxy-based, low-density structural polymeric foam (initial bulk density 0.81 g/cm³ was used for test illustration) under quasistatic and high strain rate conditions in rigid confinement. Quasistatic crushability tests were conducted in a steel confinement cell using an MTS material testing system and the high strain rate (dynamic) crushability behavior was investigated by placing a foam specimen in a steel confinement tube and then loading the specimen using two different split Hopkinson pressure bar systems, namely, a magnesium bar and steel bar. The dynamic deformation characteristics were obtained using a multi-step incremental loading procedure. It was found that these foams exhibited large uniform inelastic deformation during the confined loading. It is verified that multi-step incremental loading can be used to construct the complete stress–strain response curve for the specimens under both quasistatic and dynamic loading conditions. A phenomenological constitutive model was then applied to parametrically describe the crushability response and to determine the rate sensitivity of the foams. The rate sensitivity of yield stress was found to be around three under rigid confinement.     

玻璃球宏细观冲击特性的SHPB试验和耦合数值模拟研究

为研究玻璃球的宏细观冲击特性,该文开展了不同相对密实度玻璃球的一维霍普金森杆(SHPB)冲击试验和离散元-有限差分法耦合数值模拟研究。结果表明：一维冲击荷载下玻璃球经历初始弹性、屈服、颗粒间互锁硬化和颗粒破碎硬化四个阶段。基于耦合数值模拟发现,颗粒平均配位数随着冲击荷载时程不断增加,但增加的速率逐渐下降,其原因是配位数变化取决于孔隙压缩和以旋转为主的颗粒重排,随着试样压缩变形的发展,孔隙压缩和颗粒重排需要克服更大的颗粒间互锁效应,因此逐渐变缓。而试样孔隙率在弹性阶段基本不变,在屈服阶段和互锁硬化阶段近似线性下降,其原因是孔隙率变化受控于颗粒整体移动,弹性阶段颗粒整体移动尚未发展,屈服之后颗粒整体移动产生的孔隙压缩随荷载时程呈线性发展。冲击荷载下,颗粒位移以整体移动为主,相对位移为辅,因此,颗粒位移对试样的初始密实度不敏感。颗粒旋转需要克服周围颗粒的互锁效应,互锁效应取决于试样级配和颗粒粒径,对密实度较敏感。     

Asymmetry Behaviour between Tension and Compression for Prestrained Materials under Cyclic Loading

The prestrained metals show substantial asymmetry between tension and compression in addition tothe softening under cyclic loading, thus the cyclic creep takes place at a load-control test. The soft-ening reflects the decrease in density of dislocation and total internal stress, and the creep implies theasymmetry in back stress between tension and compression, The mechanical behaviour of the soft-ening is similar for materials with different slip modes, but their features of creep differ significantly.The creep of planar slip Cu-Zn alloy exhibits“explosively”, while that of wavy slip Cu and low car-bon steel occurs continuously and slowly. The explanation of creep behaviour via the internal dislo-cation structure was presented in this paper. According to asymmetw behaviour, it can be concludedthat the internal processes of softehing also strongly depend on the slip mode. In addition, underhigh stress amplitude the opposite asymmetries take place for Cu and Cu-Zn alloy, it indicates thatasymmetric back stresses developed in pretension have been eliminated even though the density andthe configuration of dislocations have not reached equilibrium.     

X70管线钢的室温蠕变及其对流变应力的影响

利用MTS万能试验机研究了X70管线钢在不同应力加载速率和不同加载过程下的室温蠕变现象,以及室温蠕变对流变应力的影响.结果表明,X70管线钢有明显的室温蠕变现象存在,应力加载速率和加载过程对室温蠕变变形量有明显的影响,而且室温蠕变显著提高了材料的流变应力.并根据位错理论对实验结果进行了分析解释.     

Dynamic frictional slip along an interface between plastically compressible solids

Dynamic frictional slip along an interface between plastically compressible solids is analyzed. The plane strain, small deformation initial/boundary value problem formulation and the numerical method are identical to those in Shi et al. (Int J Fract 162:51, 2010) except that here the material constitutive relation allows for plastic compressibility. The interface is characterized by a rate and state dependent friction law. The specimens have an initial compressive stress and are subject to shear loading by edge impact near the interface. Two loading conditions are analyzed, one giving rise to a crack-like mode of slip propagation and the other to a pulse-like mode of slip propagation. In both cases, the initial compressive stress is taken to vary with plastic compressibility such that the associated initial effective stress is the same for all values of plastic compressibility. The volume change for the crack-like slip mode is mainly plastic while the elastic volume change plays a larger role for the pulse-like mode. For the crack-like slip mode, the proportion of plastic dissipation in the material increases with the increasing plastic compressibility, but the effect of plastic compressibility on the energy partitioning for the pulse-like slip mode is much smaller. The predicted propagation speeds approach a speed about the dilational wave speed for both the crack-like and pulse-like slip modes and this speed is not sensitive to the value of the plastic compressibility parameter. Plastic dissipation is found to be mainly associated with the deformation induced by the loading wave rather than with the deformation arising from slip propagation. The amplitude of the slip rate in the slip pulses is found to be largely governed by the value of the initial compressive stress regardless of the value of plastic compressibility.

     

Residual fatigue life prediction based on a novel damage accumulation model considering loading history

The influence of prior low‐cycle fatigue (LCF) on the residual fatigue life was investigated experimentally. A Ni‐based alloy was cyclically loaded under stress‐controlled low‐high (LH) block loading. In the first loading step, low‐amplitude loading was performed with the stress amplitude of 283.5MPa at 710°C. Different cycles of preloading were performed, varying from 100 to 10 000. Subsequently, high‐amplitude fatigue loading was carried out with the stress amplitude of 315MPa at 800°C. Experimental results show that the previous loading was beneficial to the residual fatigue life when the consumed life fraction is below 0.2 and detrimental when the consumed life fraction is larger than 0.2. A novel nonlinear fatigue damage accumulation model was proposed to estimate the residual LCF life under LH loading path considering the effects of load sequence and preloading cycles. The proposed model provided a better life prediction than some existing models, such as Kwofie‐Rahbar model, Miner' rule, Peng model, and Ye‐Wang model. Lastly, this model was further validated using various materials under LH and high‐low block loadings.     

Influence of Compression and Shear on the Strength of Composite Laminates with Z-Pinned Reinforcement

The influence of compression and shear loads on the strength of composite laminates with z-pins is evaluated parametrically using a 2D Finite Element Code (FLASH) based on Cosserat couple stress theory. Meshes were generated for three unique combinations of z-pin diameter and density. A laminated plate theory analysis was performed on several layups to determine the bi-axial stresses in the zero degree plies. These stresses, in turn, were used to determine the magnitude of the relative load steps prescribed in the FLASH analyses. Results indicated that increasing pin density was more detrimental to in-plane compression strength than increasing pin diameter. Compression strengths of lamina without z-pins agreed well with a closed form expression derived by Budiansky and Fleck. FLASH results for lamina with z-pins were consistent with the closed form results, and FLASH results without z-pins, if the initial fiber waviness due to z-pin insertion was added to the fiber waviness in the material to yield a total misalignment. Addition of 10% shear to the compression loading significantly reduced the lamina strength compared to pure compression loading. Addition of 50% shear to the compression indicated shear yielding rather than kink band formation as the likely failure mode. Two different stiffener reinforced skin configurations with z-pins, one quasi-isotropic and one orthotropic, were also analyzed. Six unique loading cases ranging from pure compression to compression plus 50% shear were analyzed assuming material fiber waviness misalignment angles of 0, 1, and 2°. Compression strength decreased with increased shear loading for both configurations, with the quasi-isotropic configuration yielding lower strengths than the orthotropic configuration.     

Rate dependent behavior and modeling of concrete based on SHPB experiments

The dynamic behavior of concrete is studied experimentally by testing annular and solid concrete specimens using split Hopkinson pressure bar (SHPB). The dynamic increase factor (DIF) of annular samples is relatively lower than the DIF of solid samples. The dynamic behavior of concrete seems to be independent of the quasi-static strength of concrete. The mode of failure of concrete was a typical ductile failure at high strain-rates and brittle at low strain-rates. No significant influence of strain-rate on the initial elastic modulus of concrete was observed. An empirical equation is proposed for the estimation of DIF of concrete based on the experiments. A model is developed for the prediction of stress–strain curve of concrete under dynamic loading which shows good agreement with the experiments.     

Dynamic compressive behavior of unidirectional E-glass/vinylester composites

Results from an experimental investigation on the mechanical behavior of unidirectional fiber reinforced polymer composites (E-glass/vinylester) with 30%, 50% fiber volume fraction under dynamic uniaxial compression are presented. Specimens are loaded in the fiber direction using a servo-hydraulic material testing system for low strain rates and a Kolsky (split Hopkinson) pressure bar for high strain rates, up to 3000/s. The results indicate that the compressive strength of the composite increases with increasing strain rate. Post-test scanning electron microscopy is used to identify the failure modes. In uniaxial compression the specimens are split axially (followed by fiber kink band formation). Based on the experimental results and observations, an energy-based analytic model for studying axial splitting phenomenon in unidirectional fiber reinforced composites is extended to predict the compressive strength of these composites under dynamic uniaxial loading condition.